Simulation and Modelling of Smart Beams with Robust Control Subjected to Wind Induced Vibration

A. Moutsopoulou, G. Stavroulakis, T. Pouliezos

Department of Civil Engineering, Technological Educational Institute of Crete, GR- 71004 ,Heraklion, Crete, Greece.
Department of Production Engineering and Management, Technical University of Crete, GR-73100 Chania, Crete, Greece.

DOI: 10.4236/ojce.2012.23016                

Abstract

This paper presents some recent developments in modelling and numerical analysis of piezoelectric systems and controlled smart structures based on a ?nite element formulation with embedded control. The control aims at vibration suppression of the structure subjected to external disturbances, like wind and noise, under the presence of model inaccuracies, using the available measurements and controls. A smart structure under dynamic loads is analysed and comparison between results for beam with and without control is made. The numerical results show that the control strategy is very effective and suppresses the vibrations of the structure.

Keywords

Smart Structures; Finite Element Formulation; Uncertainty; Robust Performance; Reduced Order Control

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1]	K. G. Arvanitis, E. C. Zacharenakis, A. G. Soldatos and G. E. Stavroulakis, “New Trends in Optimal Structural Control. Selected Topics in Structronic and Mechatronic System,” World Scientific Publishers, Singapore, 2003, pp. 321-415. doi:10.1142/9789812795526_0008
[2]	G. Foutsitzi, D. Marinova, E. Hadjigeorgiou and G. Stavroulakis, “Robust H2 vi Bration Control of Beams with Piezoelectric Sensors and Actuators,” Proceedings of Physics and Control Conference (PhyCon03), St. Petersburg, Vol. I, 20-22 August 2003, pp. 158-163.
[3]	G. Foutsitzi, D. Marinova, E. Hadjigeorgiou and G. Stavroulakis, “Finite Element Modelling of Optimally Controlled Smart Beams,” 28Ih Summer School: Applications of Mathematics in Engineering and Economics, Sozopol, Bulgaria, 2002.
[4]	B. Miara, G. Stavroulakis and V. Valente, “Topics on Mathematics for Smart Systems,” Proceedings of the European Conference, Rome, 26-28 October 2006, World Scientific Publishers, Singapore, 2007.
[5]	G. E. Stavroulakis, G. Foutsitzi, E. Hadjigeorgiou, D. Marinova and C. C. Baniotopoulos, “Design and Robust Optimal Control of Smart Beams with Application on Vibrations Suppression,” Advances in Engineering Software, Vol. 36, No. 11-12, 2005, pp. 806-813.
[6]	H. F. Tiersten, “Linear Piezoelectric Plate Vibrations,” Plenum Press, New York, 1969.
[7]	N. Zhang and I. Kirpitchenko, “Modelling Dynamics of a Continuous Structure with a Piezoelectric Sensor/Actua- tor for Passive Structural Control,” Journal of Sound and Vibration, Vol. 249, No. 2, 2002, pp. 251-261. doi:10.1006/jsvi.2001.3792
[8]	T. T. Soong and G. D. Manolis. “Active Structures,” ASCE Journal of Structural Engineering, Vol. 113, No. 11, 1987, pp. 2290-2302. doi:10.1061/(ASCE)0733-9445(1987)113:11(2290)
[9]	M. D. Symans and M. C. Konstantinou, “Semi-Active Control System for Seismic Protection of Structure: A State-of-the-Art Review,” Engineerings Structures, Vol. 21, No. 6, 1999, pp. 469-487. doi:10.1016/S0141-0296(97)00225-3
[10]	M. Anjanappa and J. Bi, “Magnetostrictive Mini Actuators for Smart Structures for Smart Structure Applications,” Int. J. Smart Materials and Structures, Vol. 3, No. 4, 1994, pp. 383-390. doi:10.1088/0964-1726/3/4/001
[11]	K. Chandrashekara and S. Varadarajan, “Adaptive Shape Control of Composite Beams with Piezoelectric Actuators,” Intelligent Materials Systems and Structures 8, 1997, pp112-124e IEEE EMBS, San Francisco, 1-5 September 2004, pp. 2758-2761.
[12]	O. Bosgra and H. Kwakernaak, “Design Methods for Control Systems,” Course notes, Dutch Institute for Systems and Control, Vol. 67, 2001.
[13]	A. Packard, J. Doyle and G. Balas, “Linear, Multivariable Robust Control with a μ Perspective,” ASME Journal of Dynamic Systems, Measurement and Control, 50th Anniversary Issue, Vol. 115, No. 2b, 1994, pp. 310-319.
[14]	B. A. Francis, “A Course on H∞ Control Theory,” Springer-Verlag, Berlin, 1985.
[15]	J. Friedman and K. Kosmatka, “An Improved Two Node Timoshenko Beam Finite Element,” Computer and Structures, Vol. 47, No. 3, 1993, pp. 473-481. doi:10.1016/0045-7949(93)90243-7
[16]	A. Moutsopoulou, A. Pouliezos and G. E. Stavroulakis, “Modelling with Uncertainty and Robust Control of Smart Beams,” In: B. H. V. Topping and M. Papadrakakis, Eds., Proceedings of the Ninth International Conference on Computational Structures Technology, Paper 35, Civil Comp Press, Stirlingshire Scotland, Civil Comp Press, 2008. doi:10.4203/ccp.88.35
[17]	J. V. Burke, D. Henrion and M. L. Lewis, “Overton HIFOO-a MATLAB Package for Fixed-Order Controller Design and Hinf. Optimization,” Proceedings of the IFAC Symposium on Robust Control Design, Toulouse, 2006. www.cs.nyu.edu/overton/software/hifoo
[18]	C. Sisemore, A. Smaili and R. Houghton, “Passive Damping of Exible Mechanism System: Experimental and Finite Element Investigation,” The 10th World Congress of the Theory of Machines and Mechanisms, Oulu, Vol. 5, 1999, pp. 2140-2145.
[19]	A. Pouliezos, “Mimo Control Systems,” Class Notes. http://pouliezos.dpem.tuc.gr
[20]	J. V. Burke, D. Henron, A. S. Kewis and M. L. Overton, “Stabilization via Nonsmooth, Nonconvex Optimization,” IEE Automatic Control, Vol. 5, No. 11, 2006, pp. 1760- 1769. doi:10.1109/TAC.2006.884944